Bruno Fernandes prompted more questions about Rafa Benitez's
zonal marking when he headed home from a corner and there were a
few nervy moments for the Merseysiders.
But Javier Mascherano equalised with a rare strike and Ryan
Babel handed the visitors the lead before the interval.
Skipper Steven Gerrard wrapped things up in the second half.
Razvan Paduretu's corner picked out centre-back Fernandes, who
was pretty much unchallenged to head past Pepe Reina and shock the
Premier League giants.
The Steau Stadium sensed a shock and it took Mascherano's second
goal in three years to change the mood.
The Argentinian pounced on a terrible clearance to a Jamie
Carragher cross and blasted a long-distance drive past Giedrius
Arlauskis.
Mascherano's wild celebration indicated just how seriously the
2005 Champions League winners were taking the competition.
Reina had to pull off a decent stop from Razvan Paduretu and
Daniel Agger was lucky to see a ball deflect just wide off him as
the home side responded well.
But Babel edged Liverpool in front when he was the only player
moving in a static box from a Gerrard free-kick. After a touch to
bring the ball under control, he prodded it past the exposed
Arlauskis in clinical fashion.
The Romanians were twice almost undone again by Gerrard before
he finally got on the scoresheet in the 57th minute.
Yossi Benayoun's run was only partially halted and England's
likely captain against Egypt pounced on the loose ball to smash it
under Arlauskis for number three.
Benitez rested a few players with the weekend in mind but there
was no outing for Fernando Torres, who remained on the bench.
Emiliano Insua has to steal the ball off Paduretu when he
threatened to pull one back but there were few moments of concern
for Liverpool, who progressed easily enough in the end.